# A Lawnmower Problem

For my physics class we were just given an exam that asked the following:

See This Image For Reference http://dev.tinyclark.com/files/problem.png

A 12Kg lawnmower is pushed with a constant force along the 30* handle with 80N. Break the Forces into its vector components. (Assume 0 Friction)

If the lawn mower was pushed with a constant force for 20 minutes, what is the final change in momentum, what is the final change in velocity, what is the final change in kinetic energy, and how far will you have walked?

After 10 minutes, how fast will the wheels be rotating and how many rotations have they made?

How big must μ be if the actual velocity is 5m/s, and how much energy will be lost due to friction?

QUESTION

I broke the Forces into their components: Fx=70N, Fy=40N. For the next part of this problem I used F=ma, and the horizontal force of 70N and found an acceleration of 5.8m/s^2, and this is where I think I went wrong, as after this all of my numbers were insanely large.

Are these just completely unrealistic numbers, and did I do it correctly? Or did I go wrong from the start? Would anyone care to share some insight on the correct answers for this problem?

Fx = 70N || Fy = 40N

Momentum = 83,520 || Velocity = 6,960m/s

KE = 290,000,000 || Distance = 4,000,000m

Rotating Speed = 22,165rps || Total Rotations = 6,650,000

Frictional u = 1.16 || Loss of energy = 10N

• Your numbers are fine – the key is that you are to assume ‘0 friction’. If you then accelerate a lawnmower at $5.8\textrm{ ms}^{-2}$ for twenty minutes, you indeed get quite interesting results. Do you have any results for the last part of the question? I assume $\mu$ to be a friction coefficient in your conventions? – Claudius Nov 15 '12 at 20:25
• I added in the u and loss of energy that I got for my answers. I am fairly certain these are incorrect.. – Matt Clark Nov 15 '12 at 21:09

Your calculations seem correct... What is unrealistic is the information they give you. For that force you correctly deduce that the horizontal acceleration is $5.8[m/s^{2}]$, which is more than half of Earth's gravity pull in the surface. If you apply continuously such a force for such a long time you will get enormous speed, energy and momentum. Just imagine an object falling in Earth's surface for 20 minutes... You are absolutely correct but the information is not realistic.